Botox and other neuromodulators such as Dysport and Xeomin work by disrupting the connection between the muscle where it is injected and the nerve that controls that muscle, resulting in relaxation of the muscle. For facial muscles, it takes about 3 months for the body to form new connections, so it is the healing time not the effect of the Botox that determines how long the effect lasts. Under-dosing will generally produce shorter duration of effect, but over-dosing will not prolong it.
Botox will not ever provide a permanent result. Most patients achieve 3-4 months of improvement from each treatment session. We have found that prolonged use of Botox can result in a requirement for smaller amounts of Botox over time. However, people need to maintain their Botox treatment schedule to maintain the result. I hope this information is helpful.